Year: 2025
Type: preprint
Abstract: We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of bounded neighborhood diversity, bounded size of maximum induced matching or bounded cluster vertex deletion number; - n log n for the class of cographs or, more generaly, bounded modular-width, and for the class of bounded distance to cograph; and - sligthly superlinear for the class of bounded shrub-depth.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416261384
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